TY - BOOK ID - 77900806 TI - Ergodic theory of numbers AU - Dajani, Karma AU - Kraaikamp, Cor PY - 2002 SN - 1614440271 9781614440277 0883850346 9780883850343 0883850001 9780883850008 9780883850220 0883850222 PB - Washington : Mathematical Association of America, DB - UniCat KW - Ergodic theory. KW - Ergodic transformations KW - Continuous groups KW - Mathematical physics KW - Measure theory KW - Transformations (Mathematics) KW - Number theory. KW - Théorie ergodique KW - Nombres, Théorie des KW - Calculus KW - Functions of real variables UR - https://www.unicat.be/uniCat?func=search&query=sysid:77900806 AB - Ergodic Theory of Numbers is an introduction to the ergodic theory behind common number expansion, like decimal expansions, continued fractions, and many others. However, its aim does not stop there. For undergraduate students with sufficient background knowledge in real analysis and graduate students interested in the area, it is also an introduction to a "dynamical way of thinking." The questions studied here are dynamical as well as number theoretical in nature, and the answers are obtained with the help of ergodic theory. Attention is focused on concepts like measure-preserving, ergodicity, natural extension, induced transformations, and entropy. These concepts are then applied to familiar expansions to obtain old and new results in an elegant and straightforward manner. What it means to be ergodic and the basic ideas behind ergodic theory will be explained along the way. The subjects covered vary from classical to recent, which makes this book appealing to researchers as well as students. ER -